Although it didn’t seem assured at every point this season, the Celtics will absolutely be making a playoff appearance, taking on a familiar foe in the Atlanta Hawks. This weekend they will arrive in the postseason, riding a crest of incredible defensive performances. Since April 1st they’ve allowed just 95.5 points per 100 possessions, the 3rd best mark in the NBA over that stretch, and a number that would lead the league if it had been carried through since December.

While it has jumped a level in the past few weeks, the Celtics’ defense has been good all season, built primarily on two pillars. They force a lot of turnovers – on 14.6% of their opponent’s possessions, the 5th best mark in the league. They also force a lot of misses. On the season the Celtics have allowed their opponents an eFG% of 45.2%, lowest in the league this season and the 7th lowest mark in the NBA over the last ten years. Defense, and eFG% allowed, has been a staple of the Celtics since the Voltron-esque assembly of Ray Allen, Paul Pierce and Kevin Garnett, but this season has been their most effective effort.

That mark of 45.2% speaks volumes to what the Celtics’ have accomplished at the defensive end, but it also conceals some truths. Their opponents are actually shooting a respectable 44.8% on two-pointers. Their eFG% mark is inflated, or deflated as the case may be, by the fact that Celtics’ opponents are shooting just 30.4% on three-pointers this season. If that mark holds over the rest of the season it would be one of the lowest in the NBA over the last twenty years.

Measuring three-point defense is a curious thing. If we assume that every shot, no matter how ludicrous and ill-advised, has at least an infinitesimal chance of going in, than the most effective means of defense would be to keep your opponent from taking three-point shots. However, players like Jordan Crawford and Kobe Bryant blow a hole through this measurement slant with their dogged determination to continue taking three-pointers irregardless of the defense, distance from the basket, time on the clock and game situation. But just looking at the flip side of the coin, shooting percentages, does not cover the whole defensive picture either, because of some player’s tendencies to help the defense by taking bad shots, and other player’s tendencies to wait for open shots.

Ken Pomeroy has done some work with defensive 3PT% over the past few months and his conclusions may surprise people. Pomeroy works with college basketball, but his evaluation was that opponent’s 3PT% is a defense independent statistic, that defense essentially has no impact on their opponent’s 3PT%. What they can exert some measure of control over is how many attempts their opponents get. Pomeroy’s analysis is difficult to replicate with the NBA because no portion of an NBA team’s schedule represents an exact duplication of a previous portion, like you find in college basketball during conference play. Still, Pomeroy’s assertion that three-point attempts allowed is a defensive statistic of tremendous import makes sense in the NBA arena.

Assuming that a team’s true ability to keep their opponents from scoring on three-pointers is reflected in both limiting makes and limiting attempts, I tried to devise a method to examine three-point defense as a combination of both factors.

The graph below is a scatter plot, with each point representing one season of Boston’s defense against one NBA team, for example, vs. Atlanta, 2009-2010. The X-axis represents the change in the opponent’s three-point attempts per game when they played Boston, against their season average. The Y-axis represents the change in the opponent’s three-point percentage when they played Boston, against their season average. The blue points are team/season defensive performances from 2007-2008 through the 2010-2011 season. The red points are from this season.

The graph is divided up into quadrants so that each point can be quickly categorized. For example, every point in Quadrant B represents a season-long series in which the Celtics held a team to fewer three-point attempts per game than they usually take AND a lower percentage than their season average.

A point in Quadrant B, fewer attempts AND makes for your opponent, would seem to be the ultimate goal here. Obviously, any point in Quadrants A or D would represent a team that, throughout a season series with Boston, shot better than their season average; not a desirable defensive outcome.

I can see the appeal of Quadrant C – if a team isn’t making a high percentage it seems like it would be advantageous to have them shoot as often as possible. But to me this piece seems like one that is out of your control. You lower the shooting percentage of your opponents by presenting them with difficult shooting opportunities, the same way you would theoretically reduce their attempts. If your opponent ignores one half of that equation and continues to shoot, it’s a bonus, but not necessarily something that you can encourage while simultaneously holding the line on percentage. It’s not very plausible that an opponent could be presented with a shot that would appear to be an open high-percentage look, which then becomes highly contested between the player making the decision to shoot and the ball leaving their hand. If you aren’t playing the Wizards every night and don’t have the luxury of counting on your opponent to shoot themselves in the foot with shot selection, than Quadrant B seems like the ideal.

Interestingly enough 35 teams over the past five season have fallen into Quadrant C against the Celtics. 16 of those 35 points come from the 2007-2008 season, and another 9 come from this season. Quadrant C would seem to represent the results most heavily influenced by luck, and it’s no surprise that those results show up most frequently in the Celtics’ two best overall defensive seasons of the Garnett-Pierce-Allen era. That’s not to say that the Celtics’ defense hasn’t been good just that it has also, like every team but the Bobcats, at times benefited from being lucky.

There is a faint whiff of random good fortune, but we also see some patterns here, revealing the influence of intention. Since 2007-2008 the Celtics were able to hold 63.4% of their opponents below their season-long three-point percentage, across a season series. They were able to hold 60.0% of those opponents to fewer three-point attempts than their season average. This season the Celtics are holding 79.0% of their opponents to below their season-long three-point percentage and 62.0% of their opponents to fewer three-point attempts than their season average. Although the peaks of the past five years may be established by luck, the foothills have clearly been built by the Celtics’ defensive system. So what exactly are the Celtics doing to keep their opponents from scoring on the perimeter?

Breaking down X’s and O’s is not my forte, but I gave it a stab as a part of this work. I spent hours watching opponents take three-pointers against the Celtics this season, and still can’t point to any definable pattern. The Celtics challenge shots, but certainly not aggressively or consistently enough to attribute the difference to mere effort. I couldn’t find anything repetitive in the way they double-team the post, funnel penetration, or defend pick-and-rolls that would explain the difference. either There’s something there, but it may take more a more keen observer than me to find it.

Looking ahead to a matchup with the Hawks, this ability to defend the three-point line should be a huge asset. The Hawks are 11th in the league in three-point attempts per game and 5th in the league in three-point percentage. They rely heavily on those long-range shots to power their offense – on the season 23.0% of their scoring has come on three-pointers, the 8th highest total in the NBA. In their three matchups this season the Celtics have held the Hawks to an ORtg. of just 91.1. They’ve kept the Hawks efficiency down by taking away this weapon, reducing their three-point attempts by 3.2 per game, and their percentage by 6.1%. Against the Celtics, the Hawks have scored just 18.5% of their points on three-pointers. This series presents a chance for the Celtics to test their defense against a team that relies heavily on the exact shot they excel at taking away.

Even if the source of this defensive strength can’t be pinpointed exactly, its presence is undeniable. The old phrase “It’s better to be lucky than good” has weight. The Boston Celtics seem to have figured out how to achieve both, and have put themselves in a great position to do some damage in the playoffs.

it is impressive to see how journalists use all kinds of stats to prove stuff in sports (especially in U.S. sports). In my opinion they are relied upon too much, one can prove/deny anything with numbers. So the Celtics are a good 3 point defensive team? I watched the games vs the Knicks and what happened there? No statistics in the world was able to predict that, let alone that something similar won't happen in the playoffs. observation should matter more than numbers…and observation tells me we are gonna beat ATL 4-1!
Let's go Celtics!

john

That doesn't make a lot of sense. Rondo went 7-8 from free throw line one game. Does that make him Ray Allen? Jut because the knicks went off doesn't mean our 3 pt defense isn't good.

CG12

He didn't say the 3pt D isn't good, he just said that you never know what is going to happen, which is entirely true. The Hawks aren't going to get hot like that, they don't have the shooters ('Melo, JR Smith, Novak).

zach

watching the knicks game is an anecdote with results that are not representative – it in no way undermines the utilitiy of statistical analyses which reflect multiple data points which are a better predictor of future outcomes. And I agree we will beat ATL 4-1

hdavenport

Came to post this exact thing.

zach

I'm a statistics teacher and celtics fan!

felix

i'm an art teacher and celtics fan!:)

felix

so we agree on the only thing that really matters:)

by the way, what's ray's status? does anyone know?

UhOh!!

funny the result of that block in the pic was a successful 3point shot for the heat….

Anthony

Funny and True. LOL.

dslack

Very nice post, Brian.

A kind of interesting thing is that good defense, if that's indeed what's responsible, shows up here only with many many data points. The cloud of points looks nearly centered on the origin, and the shift to the lower left is much smaller than the scatter in the distribution of points.

It IS interesting that there's only one red point in quadrant D, although that might just(/mostly) be luck.

akismet-9bb87bd2c168ef53382eb14742d5f8bb

Nice post. Numbers do get tiring sometimes. It may not be supported by numbers, but a keen observer (as you said) can see things develop in a way numbers cannot quantify.

For instance, everyone knows that a 3-pt shot is less likely to go in than a 2-pt shot, and a 2-pt shot from 16 feet is less likely to go in than a dunk or layup… Well, the Celtics' defensive philosophy is to force teams to take difficult shots that have less of a chance of going in. Not only do they close out and contest well, but they force teams to take undesirable shots, usually at the end of a shot clock. With KG directing traffic from the post, the D funnels the offense where they want it to go. They keep guys out of the paint, cut off interior passing lanes, and force the pick-and-roll as far out as possible, usually around the 3-pt line. By doing these things, they're forcing offenses to attempt shots at or near the 3-pt line. The long-distance jump shots (and threes) taken by opponents are usually the last resort shot. By the time they take that shot, the Celtics have already taken away the first, second, and third options. Most threes hit against the Celtics come from either 1) end of the shot clock dribbling and pull-up shots (i.e. Carmelo or Kobe) or 2) crisp passing to the weak side where the right 3-pt gunner is lying in wait (i.e. when a James Jones or someone is just standing in the opposite corner awaiting the pass). Once in a while, a shot is going to fall. Difficult to consistently stop guys like Melo and Kobe, and the second option usually only occurs when someone on the C's missed their defensive rotation.

The Celtics also benefit from having guards like Rondo and Bradley who pick up opposing guards well beyond the 3-pt line, denying any rhythmic pull-up threes. They don't sag off and let guards shoot coming up off the dribble.

The Knicks game was an aberration. The Knicks hit uncontested and contested threes at a rate not sustainable. That's the kind of 3-pt shooting game that happens for each team once per season.

High Rollers

Give all the credit to the C’s because they’re the ones doing the work out there, figuring things out night after night.

That said, I have a theory. Without all those heavy duty centers we used boast, opponents are licking their chops each night at the prospect of plowing the paint. The C’s never really overcame that but rather worked around it. We got better at, one might go so far as to say perfected, taxing the guys on the perimeter. Those would be the guards, the quarterbacks, the decision makers. We are simply wearing them out and it’s having a domino effect down into the paint, where they assume they have the upperhand most nights. By the time our guys are on a string, the other guys don’t know what hit ‘em. Basically it is the D, a D that adapted and evolved from a weakness to a strength over the course of 4 months. Because our players and coaching staff are wicked smart.

High Rollers

It’s that cutting the head off the snake business.

Phil

Nice post, I like delving into the depths of the stats a good amount from time to time. Not surprised that there's some luck involved in a historic number, but its also good to see that there's some real substance to it as well. If the Celtics can continue doing what they've been doing, they'll be fine. Sometimes the shots will still fall, but a lot more games ended in the B plot than the others, and that's what you want.

michaelmarlow

Interesting premise about the number of 3pt attempts being the important indicator; I could buy that. I am curious why Quadrant 3 is necessarily the "luck" quadrant, however. Even if you catch a team on an off-night, it's not like a bad night at the free throw line; the defense can still influence in part what's happening. You can encourage bad shooters to keep chucking, for instance (maybe not on 3's, but hello, Josh Smith! is the first guy that comes to mind). Is it not feasible that the defense could be forcing a lot of late-clock and/or highly contested shots that end up as 3's? Or maybe you're not saying it is "necessarily" the luck quadrant, but the most logical to be interpreted as such…not sure how that could easily be determined though.

Another point I think you have to take into account is that an NBA 3 point shot is a much different shot than a college 3 (especially when you get out of the corners).

hdavenport

Echoing what High Rollers was saying about other teams "licking their chops" about Boston getting smaller inside: opponents are taking 2-3 more attempts at the rim against Boston this year (25.8) than any year of the Big Three era. However, they're actually converting inside shots at about the same rate as in previous years (58.5%, even less than last year).

Seems like opposing teams are focusing their attack against Boston at the rim, but finding to their dismay that Boston's system of help defense is frustrating drive and post-up plays just as much as it did in previous years, even though they've gotten smaller. That would lead to a result of other teams taking fewer threes (because they're trying to go inside) and making fewer of them (because the ones they do take are at the end of the shot clock after an aborted attempt to get to the rim, as akismet pointed out).